While the specific situation described here was likely resolved years ago, I thought I would add some info here that could be useful to others who stumble upon this later. Disclaimer: I am neither an agent nor an attorney, but am generally familiar with service dog law.
The obligations of housing providers to accommodate animals that benefit individuals with disabilities are described here: https://portal.hud.gov/hudportal/documents/huddoc%3Fid%3Dservanimals_ntcfheo2013-01.pdf The regulations apply equally to trained service dogs and to other animals that help individuals with disabilities (commonly referred to as "emotional support animals", although I have occasionally heard them referred to as therapy animals as well).
Both homeowners' associations and landlords need to comply with these regulations.
Short answer: an HOA and (most) landlords must waive no-pets policies and size restrictions for animals that benefit individuals with disabilities. So on the face of it, the HOA's actions described here are illegal.
However, the HOA is within their rights to require the dog be removed on the basis of the fact that it appears to be a direct threat to the health and safety of others. A court would most likely find that a large dog's snapping at someone is sufficient evidence that the dog is a direct threat, regardless of the fact that the dog was being teased at the time.
I hope this helps.